Solve f(x)=(x+3)^2(x+1)(x-1)

$$f ( x ) = ( x + 3 ) ^ { 2 } ( x + 1 ) ( x - 1 )$$

Evaluate

$$\left(x^{2}-1\right)\left(x+3\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3\right)^{2}.

$$\left(x^{2}+6x+9\right)\left(x+1\right)\left(x-1\right)$$

Use the distributive property to multiply x^{2}+6x+9 by x+1 and combine like terms.

$$\left(x^{3}+7x^{2}+15x+9\right)\left(x-1\right)$$

Use the distributive property to multiply x^{3}+7x^{2}+15x+9 by x-1 and combine like terms.

$$x^{4}+6x^{3}+8x^{2}-6x-9$$

Expand

$$x^{4}+6x^{3}+8x^{2}-6x-9$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3\right)^{2}.

$$\left(x^{2}+6x+9\right)\left(x+1\right)\left(x-1\right)$$

Use the distributive property to multiply x^{2}+6x+9 by x+1 and combine like terms.

$$\left(x^{3}+7x^{2}+15x+9\right)\left(x-1\right)$$

Use the distributive property to multiply x^{3}+7x^{2}+15x+9 by x-1 and combine like terms.

$$x^{4}+6x^{3}+8x^{2}-6x-9$$